Trump tops the field with 39%, according to the poll of Republican and Republican-leaning registered voters. That's more than double the share backing Cruz, who, at 18%, has inched up 2 points since the last CNN/ORC poll, which was taken in late November.

Trump has been a constant atop the polls since his ascent to the lead in July, and this new poll marks the first time Cruz stands significantly apart from the other candidates vying for the nomination. Behind those two, Ben Carson and Florida Sen. Marco Rubio have each slipped a few points and now stand tied at 10%.

A Quinnipiac University poll released Tuesday found a tighter race between Trump and Cruz, a finding that clashes with most other recent polling on the national race. It is one of only two live interviewer national polls released since Thanksgiving that found Trump with a lead smaller than 10 points. Across the 10 polls released during that time, Trump's lead over Cruz averages 16 points.

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The CNN/ORC poll was conducted after the Republican debate hosted by CNN and Facebook in Las Vegas on December 15. Among those Republicans who say they watched, 33% say Trump did the best job in the debate, 28% Cruz, 13% Rubio. New Jersey Gov. Chris Christie follows with 6%. Former Florida Gov. Jeb Bush, widely seen as needing a strong debate performance to boost his standing in the polls, was rated best by just 1% of debate watchers.

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Six in 10 Republican voters in the poll now say there are one or two candidates they'd prefer to see win over the rest of the field, up from 48% who had identified favorites in July. That consolidation is reflected in voters' overall preferences. This marks the second CNN/ORC poll in a row in which more than three-quarters of Republicans now support one of the top four candidates (77% choose one of Trump, Cruz, Carson or Rubio), and 57% now support one of the top two candidates. That latter figure marks the highest share for any two candidates combined this cycle.

Trump's standing in the race for the nomination is bolstered by widely held trust that he can best handle the top issues facing the nation. Trump holds massive advantages over the rest of the field as the candidate best able to handle the economy (57% Trump, his next closest competitors are Cruz at 8%, Rubio at 7%, Carson at 6% and Bush at 5%), illegal immigration (55% trust Trump, followed by Cruz at 15%, Rubio at 10%), and ISIS (47% prefer Trump, 21% Cruz, 7% Bush and 6% Christie).

And Republicans are coming around to the idea that the Republican Party has its best shot at winning the presidency by nominating the New York real estate mogul. Overall, 46% of GOP voters say the Republicans have a better chance to win in 2016 with Trump as the party's nominee, while 50% say the GOP has a better shot with someone else at the top of the ticket. In August, just 38% said Trump brought the Republicans their best chances.

Perhaps obviously, Trump's supporters are most likely to think the GOP has its best shot with Trump as its nominee (85% say so), but even among those who aren't current supporters, 21% think Trump would be better than the alternative.

Among those who say the party has a better shot with someone other than Trump, Cruz is the preferred candidate, 25% would like to see him win the nomination, 16% Rubio, 13% Carson, 9% are Trump backers, 8% Kentucky Sen. Rand Paul, 7% Christie and 4% each Bush and Kasich.

There are signs in the poll that Cruz's debate performance may have helped improve his appeal. Though he remains well behind Trump, Cruz gained ground on the front-runner on handling illegal immigration and ISIS, both a central focus of the debate's questions, while Rubio and Carson faded on both issues. Cruz's favorability rating has jumped 22 points among Republican voters since September, and he now holds the highest favorability rating among Republican voters of any of the seven candidates tested. He's also posted the largest increase in favorability rating among all adults since September, climbing from 27% favorable in September to 45% now, an 18-point gain. Trump (+8) and Rubio (+14) posted smaller increases.

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More Republican voters (62%) say Cruz has the right experience to be president than say so about Trump (57%) or Rubio (53%), and two-thirds say Cruz shares their values and is someone they would be proud to have as president (66% each). Slightly fewer say either sentiment applies to Trump (63% values, 60% proud) or Rubio (64% values, 62% proud).

Education remains a stark dividing line among Republicans, but since last month Trump has gained ground with the party's college graduates. In the new poll, 27% of GOP voters with degrees back Trump, up from 18% in the late-November poll. Among those without degrees, 46% back Trump, the same share as in November. Non-college voters could prove to be an Achilles heel for Rubio, who holds just 6% support among that group compared with 19% among those who hold degrees.

The CNN/ORC poll was conducted by telephone December 17-21 among a random national sample of 1,018 adults. Results for the full sample have a margin of sampling error of plus or minus 3 percentage points. For results among the 438 registered voters who are Republicans or independents who lean toward the Republican Party, the margin of sampling error is plus or minus 4.5 percentage points.